For the incompressible Stokes problem, we firstly propose mortar element method for Q_1~(rot)/Q_0 element for it, and get the optimal error estimate by proving the inf-sup condition of the discrete saddle point problem.
Under the Ostrowski-Kantorovich condi- tions a successful existence-convergence theorem of iteration procedures for 0≤μ≤2 is estab- lished. Meanwhile,the optimal error estimates for 0≤μ≤2 are obtained.
Stability and convergence of the totally discrete finite element method for a class of second order nonlinear coupled equations arising in the thermoelastic theory are discussed, and the optimal error estimates between the exact solution and the FEM solutions in H~1, L~2, L~∞ norm are obtained.
Moreover, we apply the CNR element to the nearly incompressible planar elasticity problem, and obtain uniformly optimal error estimates in both energy and L2 norm, which is independent of the Lame constant λ.
In this paper, by use of integration of boundary as degrees of freedom, a class of product type nonconforming arbitrarily quadrilateral elements are constructed. The optimal error estimation for solving Stokes equations is obtained, and some known elements are our special cases.
In this paper,Galerkin approximations of Second order hyperbolic equation is studied with the anisotropic modified rotated Q1-element. By means of integral identities and boundary estimates techniques,the optional error estimation is presented for hyperbolic equation.
This allows to obtain an optimal error estimate, also verified by numerical experiments.
We prove an optimal error estimate and give illustrative numerical example.
The convergence and optimal error estimate for the approximate solution and numerical experiment are provided.
Finally, the optimal error estimate in the energy norm is derived for the method.
In this paper, a Signorini problem in three dimensions is reduced to a variational inequality on the boundary, and a boundary element method is described for the numerical approximation of its solution; an optimal error estimate is also given.
Optimal error estimates in L∞(J;H1(ω)) are proved, which implies an essential improvement to existed results.
Optimal error estimates in L2 and H1 norm are obtained for the approximation solution.
By use of the special properties of this element, and by introducing the complementary space and a series of novel techniques, the optimal error estimates of the energy norm and the L2-norm are obtained.
Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation
For the multidimensional heat equation in a parallelepiped, optimal error estimates inL2(Q) are derived.